Chaotic homeomorphisms of R-n lifted from torus homeomorphisms

We establish the existence of self-homeomorphisms of R-n, n greater than or equal to 2, which are chaotic in the sense of Devaney, preserve volume and are spatially periodic. Moreover, we show that in the space of volume-pres erving homeomorphisms of the n-torus with mean rotation zero, those with ch aotic lifts to RR are dense, with respect to the uniform topology. An appli cation is given fbr fixed points of 2-dimensional torus homeomorphisms (Con ley-Zehnder-Franks Theorem).